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                    <h1 class="description center-align post-title">机器学习算法（四）：降维算法PCA和SVD</h1>
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<p>这一系列的笔记水得很，开始兴致冲冲，潦草结束都算不上，半途而废。虽然这样做有点帮助，但是最重要的还是<strong>思考实践</strong>，不是为了做笔记而做笔记，这一波笔记，到最后简直要吐了，不知道为了什么，吐得我几天都不想碰了。<strong>参考菜菜视频教程</strong>，还不如直接看pdf。等我做了好web项目再战机器学习。</p>
</blockquote>
<h2 id="一、概述"><a href="#一、概述" class="headerlink" title="一、概述"></a>一、概述</h2><h4 id="1-从什么叫“维度”说开来"><a href="#1-从什么叫“维度”说开来" class="headerlink" title="1.从什么叫“维度”说开来"></a>1.从什么叫“维度”说开来</h4><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215043.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215537.png"></p>
<h4 id="2-sklearn中的降维算法"><a href="#2-sklearn中的降维算法" class="headerlink" title="2.sklearn中的降维算法"></a>2.sklearn中的降维算法</h4><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215626.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215655.png"></p>
<h2 id="二、-PCA与SVD"><a href="#二、-PCA与SVD" class="headerlink" title="二、 PCA与SVD"></a>二、 PCA与SVD</h2><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215746.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215815.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215831.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215846.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215906.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309215941.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220009.png"></p>
<ol>
<li>调用库和模块</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.decomposition import PCA<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre>
<ol start="2">
<li>提取数据集</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">iris = load_iris()
y = iris.target
X = iris.data
#作为数组，X是几维？
X.shape#(150, 4)
#作为数据表或特征矩阵，X是几维？
import pandas as pd
pd.DataFrame(X).head()
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="3">
<li>建模</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#调用PCA
pca = PCA(n_components=2)           #实例化
pca = pca.fit(X)                    #拟合模型
X_dr = pca.transform(X)             #获取新矩阵
 
X_dr
#也可以fit_transform一步到位
#X_dr = PCA(2).fit_transform(X)
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="4">
<li>可视化</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#要将三种鸢尾花的数据分布显示在二维平面坐标系中，对应的两个坐标（两个特征向量）应该是三种鸢尾花降维后的x1和x2，怎样才能取出三种鸢尾花下不同的x1和x2呢？
 
X_dr[y == 0, 0] #这里是布尔索引，看出来了么？
 
#要展示三中分类的分布，需要对三种鸢尾花分别绘图
#可以写成三行代码，也可以写成for循环
"""
plt.figure()
plt.scatter(X_dr[y==0, 0], X_dr[y==0, 1], c="red", label=iris.target_names[0])
plt.scatter(X_dr[y==1, 0], X_dr[y==1, 1], c="black", label=iris.target_names[1])
plt.scatter(X_dr[y==2, 0], X_dr[y==2, 1], c="orange", label=iris.target_names[2])
plt.legend()
plt.title('PCA of IRIS dataset')
plt.show()
"""
 
colors = ['red', 'black', 'orange']
iris.target_names
 
plt.figure()
for i in [0, 1, 2]:
    plt.scatter(X_dr[y == i, 0]
                ,X_dr[y == i, 1]
                ,alpha=.7#指画出的图像的透明度
                ,c=colors[i]
                ,label=iris.target_names[i]
               )
plt.legend()#图例
plt.title('PCA of IRIS dataset')
plt.show()
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220206.png"></p>
<blockquote>
<p>鸢尾花的分布被展现在我们眼前了，明显这是一个分簇的分布，并且每个簇之间的分布相对比较明显，也许 versicolor和virginia这两种花之间会有一些分类错误，但setosa肯定不会被分错。这样的数据很容易分类，可以遇 见，KNN，随机森林，神经网络，朴素贝叶斯，Adaboost这些分类器在鸢尾花数据集上，未调整的时候都可以有 95%上下的准确率。</p>
</blockquote>
<ol start="6">
<li>探索降维后的数据</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#属性explained_variance_，查看降维后每个新特征向量上所带的信息量大小（可解释性方差的大小）
pca.explained_variance_#查看方差是否从大到小排列，第一个最大，依次减小   array([4.22824171, 0.24267075])
 
#属性explained_variance_ratio，查看降维后每个新特征向量所占的信息量占原始数据总信息量的百分比
#又叫做可解释方差贡献率
pca.explained_variance_ratio_#array([0.92461872, 0.05306648])
#大部分信息都被有效地集中在了第一个特征上
 
pca.explained_variance_ratio_.sum()#0.977685206318795<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="7">
<li>选择最好的n_components：累积可解释方差贡献率曲线</li>
</ol>
<blockquote>
<p>当参数n_components中不填写任何值，则默认返回min(X.shape)个特征，一般来说，样本量都会大于特征数目， 所以什么都不填就相当于转换了新特征空间，但没有减少特征的个数。一般来说，不会使用这种输入方式。但我们 却可以使用这种输入方式来画出累计可解释方差贡献率曲线，以此选择最好的n_components的整数取值。 </p>
<p>累积可解释方差贡献率曲线是一条以降维后保留的特征个数为横坐标，降维后新特征矩阵捕捉到的可解释方差贡献 率为纵坐标的曲线，能够帮助我们决定n_components最好的取值。</p>
</blockquote>
<pre class="line-numbers language-none"><code class="language-none">import numpy as np
pca_line = PCA().fit(X)
# pca_line.explained_variance_ratio_#array([0.92461872, 0.05306648, 0.01710261, 0.00521218])
plt.plot([1,2,3,4],np.cumsum(pca_line.explained_variance_ratio_))
plt.xticks([1,2,3,4]) #这是为了限制坐标轴显示为整数
plt.xlabel("number of components after dimension reduction")
plt.ylabel("cumulative explained variance ratio")
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220449.png"></p>
<h6 id="最大似然估计自选超参数"><a href="#最大似然估计自选超参数" class="headerlink" title="最大似然估计自选超参数"></a>最大似然估计自选超参数</h6><blockquote>
<p>除了输入整数，n_components还有哪些选择呢？之前我们提到过，矩阵分解的理论发展在业界独树一帜，勤奋智 慧的数学大神Minka, T.P.在麻省理工学院媒体实验室做研究时找出了让PCA用最大似然估计(maximum likelihood estimation)自选超参数的方法，输入“mle”作为n_components的参数输入，就可以调用这种方法。</p>
</blockquote>
<pre class="line-numbers language-none"><code class="language-none">pca_mle = PCA(n_components="mle")#mle缺点计算量大
pca_mle = pca_mle.fit(X)
X_mle = pca_mle.transform(X)
 
X_mle#3列的数组
#可以发现，mle为我们自动选择了3个特征
 
pca_mle.explained_variance_ratio_.sum()#0.9947878161267247
#得到了比设定2个特征时更高的信息含量，对于鸢尾花这个很小的数据集来说，3个特征对应这么高的信息含量，并不
# 需要去纠结于只保留2个特征，毕竟三个特征也可以可视化

# 0.9947878161267247<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h6 id="按信息量占比选超参数"><a href="#按信息量占比选超参数" class="headerlink" title="按信息量占比选超参数"></a>按信息量占比选超参数</h6><blockquote>
<p>输入[0,1]之间的浮点数，并且让参数svd_solver ==’full’，表示希望降维后的总解释性方差占比大于n_components 指定的百分比，即是说，希望保留百分之多少的信息量。比如说，如果我们希望保留97%的信息量，就可以输入 n_components = 0.97，PCA会自动选出能够让保留的信息量超过97%的特征数量。</p>
</blockquote>
<pre class="line-numbers language-none"><code class="language-none">pca_f = PCA(n_components=0.97,svd_solver="full")#svd_solver="full"不能省略
pca_f = pca_f.fit(X)
X_f = pca_f.transform(X)
X_f 
pca_f.explained_variance_ratio_#array([0.92461872, 0.05306648])<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h4 id="PCA中的SVD"><a href="#PCA中的SVD" class="headerlink" title="PCA中的SVD"></a>PCA中的SVD</h4><h6 id="PCA中的SVD哪里来？"><a href="#PCA中的SVD哪里来？" class="headerlink" title="PCA中的SVD哪里来？"></a>PCA中的SVD哪里来？</h6><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220734.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220748.png"></p>
<pre class="line-numbers language-none"><code class="language-none">#X.shape()#(m,n)
PCA(2).fit(X).components_.shape#(2, 4)

PCA(2).fit(X).components_#V(k,n)
# array([[ 0.36138659, -0.08452251,  0.85667061,  0.3582892 ],
#        [ 0.65658877,  0.73016143, -0.17337266, -0.07548102]])<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h6 id="重要参数svd-solver-与-random-state"><a href="#重要参数svd-solver-与-random-state" class="headerlink" title="重要参数svd_solver 与 random_state"></a>重要参数svd_solver 与 random_state</h6><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220905.png"></p>
<h6 id="重要属性components"><a href="#重要属性components" class="headerlink" title="重要属性components_"></a>重要属性components_</h6><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309220930.png"></p>
<ol>
<li>导入需要的库和模块</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.datasets import fetch_lfw_people#7个人的1000多张人脸图片组成的一组人脸数据
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
import numpy as np
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="2">
<li>实例化数据集，探索数据</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">faces = fetch_lfw_people(min_faces_per_person=60)#实例化   min_faces_per_person=60：每个人取出60张脸图
faces#一个字典形式的数据

faces.images.shape#（1277,62,47）  1277是矩阵中图像的个数，62是每个图像的特征矩阵的行，47是每个图像的特征矩阵的列
#怎样理解这个数据的维度？
faces.data.shape#（1277,2914）   行是样本，列是样本相关的所有特征：2914 = 62 * 47
#换成特征矩阵之后，这个矩阵是什么样？
X = faces.data<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="3">
<li>看看图像什么样？将原特征矩阵进行可视化</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#数据本身是图像，和数据本身只是数字，使用的可视化方法不同
 
#创建画布和子图对象
fig, axes = plt.subplots(4,5#4行5列个图
                        ,figsize=(8,4)#figsize指的是图的尺寸
                        ,subplot_kw = {"xticks":[],"yticks":[]} #不要显示坐标轴
                        )
fig#指的是画布
 
axes
#不难发现，axes中的一个对象对应fig中的一个空格
#我们希望，在每一个子图对象中填充图像（共24张图），因此我们需要写一个在子图对象中遍历的循环
axes.shape#（4,5）
 
#二维结构，可以有两种循环方式，一种是使用索引，循环一次同时生成一列上的四个图
#另一种是把数据拉成一维，循环一次只生成一个图
#在这里，究竟使用哪一种循环方式，是要看我们要画的图的信息，储存在一个怎样的结构里
#我们使用 子图对象.imshow 来将图像填充到空白画布上
#而imshow要求的数据格式必须是一个(m,n)格式的矩阵，即每个数据都是一张单独的图
#因此我们需要遍历的是faces.images，其结构是(1277, 62, 47)
#要从一个数据集中取出24个图，明显是一次性的循环切片[i,:,:]来得便利
#因此我们要把axes的结构拉成一维来循环

# [*axes.flat]#2维
axes.flat#降低一个维度
# [*axes.flat] #1维

enumerate(axes.flat)
 
#填充图像
for i, ax in enumerate(axes.flat):
    ax.imshow(faces.images[i,:,:] 
              ,cmap="gray" #选择色彩的模式
            )
 
# cmap参数取值选择各种颜色：https://matplotlib.org/tutorials/colors/colormaps.html<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309221427.png"></p>
<ol start="4">
<li>建模降维，提取新特征空间矩阵</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#原本有2900维，我们现在来降到150维
pca = PCA(150).fit(X)#这里X = faces.data，不是faces.images.shape ,因为sklearn只接受2维数组降，不接受高维数组降
# x_dr = pca.transform(X)
# x_dr.shape#(1277,150)

V = pca.components_#新特征空间
V.shape#V（k，n）   (150, 2914)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="5">
<li>将新特征空间矩阵可视化</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">fig, axes = plt.subplots(3,8,figsize=(8,4),subplot_kw = {"xticks":[],"yticks":[]})
 
for i, ax in enumerate(axes.flat):
    ax.imshow(V[i,:].reshape(62,47),cmap="gray")
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309221511.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309221526.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309225625.png"></p>
<ol>
<li>导入需要的库和模块</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.datasets import fetch_lfw_people
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
import numpy as np<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="2">
<li>导入数据，探索数据</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">faces = fetch_lfw_people(min_faces_per_person=60)
faces.images.shape
#怎样理解这个数据的维度？
faces.data.shape
#换成特征矩阵之后，这个矩阵是什么样？
X = faces.data
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="3">
<li>建模降维，获取降维后的特征矩阵X_dr</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">pca = PCA(150)#实例化
X_dr = pca.fit_transform(X)#拟合+提取结果
X_dr.shape
# (1348, 150)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="4">
<li>将降维后矩阵用inverse_transform返回原空间</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">X_inverse = pca.inverse_transform(X_dr)
 
X_inverse.shape#(1348, 2914)

faces.images.shape#(1348, 62, 47)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="5">
<li>将特征矩阵X和X_inverse可视化</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">fig, ax = plt.subplots(2,10,figsize=(10,2.5)
                      ,subplot_kw={"xticks":[],"yticks":[]}
                     )
 
#和2.3.3节中的案例一样，我们需要对子图对象进行遍历的循环，来将图像填入子图中
#那在这里，我们使用怎样的循环？
#现在我们的ax中是2行10列，第一行是原数据，第二行是inverse_transform后返回的数据
#所以我们需要同时循环两份数据，即一次循环画一列上的两张图，而不是把ax拉平
 
for i in range(10):
    ax[0,i].imshow(faces.images[i,:,:],cmap="binary_r")
    ax[1,i].imshow(X_inverse[i].reshape(62,47),cmap="binary_r")
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309225843.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309225900.png"></p>
<ol>
<li>导入所需要的库和模块</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.datasets import load_digits
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
import numpy as np
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="2">
<li>导入数据，探索数据</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">digits = load_digits()
digits.data.shape#(1797, 64)
set(digits.target.tolist())#查看target有哪几个数  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

digits.images.shape#(1797, 8, 8)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="3">
<li>定义画图函数</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">def plot_digits(data):
    #data的结构必须是（m,n），并且n要能够被分成（8,8）这样的结构
    fig, axes = plt.subplots(4,10,figsize=(10,4)
                            ,subplot_kw = {"xticks":[],"yticks":[]}
                            )
    for i, ax in enumerate(axes.flat):
        ax.imshow(data[i].reshape(8,8),cmap="binary")
        
plot_digits(digits.data)
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230029.png"></p>
<ol start="4">
<li>为数据加上噪音</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">rng = np.random.RandomState(42)
 
#在指定的数据集中，随机抽取服从正态分布的数据
#两个参数，分别是指定的数据集，和抽取出来的正太分布的方差
noisy = rng.normal(digits.data,2)#np.random.normal(digits.data,2)
 
plot_digits(noisy)
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230057.png"></p>
<ol start="5">
<li>降维</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">pca = PCA(0.5,svd_solver='full').fit(noisy)
X_dr = pca.transform(noisy)
X_dr.shape#(1797, 6)
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre>
<ol start="6">
<li>逆转降维结果，实现降噪</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">without_noise = pca.inverse_transform(X_dr)
plot_digits(without_noise)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230118.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230212.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230311.png"></p>
<h4 id="案例：PCA对手写数字数据集的降维"><a href="#案例：PCA对手写数字数据集的降维" class="headerlink" title="案例：PCA对手写数字数据集的降维"></a>案例：PCA对手写数字数据集的降维</h4><blockquote>
<p>还记得我们上一周在讲特征工程时，使用的手写数字的数据集吗？数据集结构为(42000, 784)，用KNN跑一次半小 时，得到准确率在96.6%上下，用随机森林跑一次12秒，准确率在93.8%，虽然KNN效果好，但由于数据量太大， KNN计算太缓慢，所以我们不得不选用随机森林。我们使用了各种技术对手写数据集进行特征选择，最后使用嵌入 法SelectFromModel选出了324个特征，将随机森林的效果也调到了96%以上。但是，因为数据量依然巨大，还是 有300多个特征。今天，我们就来试着用PCA处理一下这个数据，看看效果如何。</p>
</blockquote>
<ol>
<li>导入需要的模块和库</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.decomposition import PCA
from sklearn.ensemble import RandomForestClassifier as RFC
from sklearn.model_selection import cross_val_score
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="2">
<li>导入数据，探索数据</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">data = pd.read_csv(r".\digit recognizor.csv")
 
X = data.iloc[:,1:]
y = data.iloc[:,0]
 
X.shape#(42000, 784)
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="3">
<li>画累计方差贡献率曲线，找最佳降维后维度的范围</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">pca_line = PCA().fit(X)
plt.figure(figsize=[20,5])
plt.plot(np.cumsum(pca_line.explained_variance_ratio_))
plt.xlabel("number of components after dimension reduction")
plt.ylabel("cumulative explained variance ratio")
plt.show()
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230444.png"></p>
<ol start="4">
<li>降维后维度的学习曲线，继续缩小最佳维度的范围</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#======【TIME WARNING：2mins 30s】======#
 
score = []
for i in range(1,101,10):
    X_dr = PCA(i).fit_transform(X)
    once = cross_val_score(RFC(n_estimators=10,random_state=0)
                           ,X_dr,y,cv=5).mean()
    score.append(once)
plt.figure(figsize=[20,5])
plt.plot(range(1,101,10),score)
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230519.png"></p>
<ol start="5">
<li>细化学习曲线，找出降维后的最佳维度</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">score = []
for i in range(10,25):
    X_dr = PCA(i).fit_transform(X)
    once = cross_val_score(RFC(n_estimators=10,random_state=0),X_dr,y,cv=5).mean()
    score.append(once)
plt.figure(figsize=[20,5])
plt.plot(range(10,25),score)
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230634.png"></p>
<ol start="6">
<li>导入找出的最佳维度进行降维，查看模型效果</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">X_dr = PCA(22).fit_transform(X)
 
#======【TIME WARNING:1mins 30s】======#
cross_val_score(RFC(n_estimators=100,random_state=0),X_dr,y,cv=5).mean()
# 0.946524472295366<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230717.png"></p>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.neighbors import KNeighborsClassifier as KNN
cross_val_score(KNN(),X_dr,y,cv=5).mean()#KNN()的值不填写默认=5    0.9698566872605972
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>
<ol start="8">
<li>KNN的k值学习曲线</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#======【TIME WARNING: 】======#

score = []
for i in range(10):
    X_dr = PCA(22).fit_transform(X)
    once = cross_val_score(KNN(i+1),X_dr,y,cv=5).mean()
    score.append(once)
plt.figure(figsize=[20,5])
plt.plot(range(10),score)
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230806.png"></p>
<ol start="9">
<li>定下超参数后，模型效果如何，模型运行时间如何？</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">cross_val_score(KNN(4),X_dr,y,cv=5).mean()#KNN()的值不填写默认=5
 
 
#=======【TIME WARNING: 3mins】======#
%%timeit
cross_val_score(KNN(4),X_dr,y,cv=5).mean()
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<blockquote>
<p>可以发现，原本785列的特征被我们缩减到23列之后，用KNN跑出了目前位置这个数据集上最好的结果。再进行更 细致的调整，我们也许可以将KNN的效果调整到98%以上。PCA为我们提供了无限的可能，终于不用再因为数据量 太庞大而被迫选择更加复杂的模型了！</p>
</blockquote>
<h2 id="三、附录"><a href="#三、附录" class="headerlink" title="三、附录"></a>三、附录</h2><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230859.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230929.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230944.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309230956.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210309231005.png"></p>

                
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                    };
                }).get();
                var $input = document.getElementById(search_id);
                var $resultContent = document.getElementById(content_id);
                $input.addEventListener('input', function () {
                    var str = '<ul class=\"search-result-list\">';
                    var keywords = this.value.trim().toLowerCase().split(/[\s\-]+/);
                    $resultContent.innerHTML = "";
                    if (this.value.trim().length <= 0) {
                        return;
                    }
                    // perform local searching
                    datas.forEach(function (data) {
                        var isMatch = true;
                        var data_title = data.title.trim().toLowerCase();
                        var data_content = data.content.trim().replace(/<[^>]+>/g, "").toLowerCase();
                        var data_url = data.url;
                        data_url = data_url.indexOf('/') === 0 ? data.url : '/' + data_url;
                        var index_title = -1;
                        var index_content = -1;
                        var first_occur = -1;
                        // only match artiles with not empty titles and contents
                        if (data_title !== '' && data_content !== '') {
                            keywords.forEach(function (keyword, i) {
                                index_title = data_title.indexOf(keyword);
                                index_content = data_content.indexOf(keyword);
                                if (index_title < 0 && index_content < 0) {
                                    isMatch = false;
                                } else {
                                    if (index_content < 0) {
                                        index_content = 0;
                                    }
                                    if (i === 0) {
                                        first_occur = index_content;
                                    }
                                }
                            });
                        }
                        // show search results
                        if (isMatch) {
                            str += "<li><a href='" + data_url + "' class='search-result-title'>" + data_title + "</a>";
                            var content = data.content.trim().replace(/<[^>]+>/g, "");
                            if (first_occur >= 0) {
                                // cut out 100 characters
                                var start = first_occur - 20;
                                var end = first_occur + 80;
                                if (start < 0) {
                                    start = 0;
                                }
                                if (start === 0) {
                                    end = 100;
                                }
                                if (end > content.length) {
                                    end = content.length;
                                }
                                var match_content = content.substr(start, end);
                                // highlight all keywords
                                keywords.forEach(function (keyword) {
                                    var regS = new RegExp(keyword, "gi");
                                    match_content = match_content.replace(regS, "<em class=\"search-keyword\">" + keyword + "</em>");
                                });

                                str += "<p class=\"search-result\">" + match_content + "...</p>"
                            }
                            str += "</li>";
                        }
                    });
                    str += "</ul>";
                    $resultContent.innerHTML = str;
                });
            }
        });
    };

    searchFunc('/search.xml', 'searchInput', 'searchResult');
});
</script>

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